Horizontal Diaphragms

1
Horizontal Diaphragms

• by Bart Quimby, P.E., Ph.D
• UAA Civil Engineering
• CE 434 - Timber Design

2
Lateral Forces

• Lateral forces result from either wind loading or
  seismic motion.
• In either case, the diaphragms are generally
  loaded with distributed loads.
• The example here is more closely associated with
  wind loading.

3
The Building
4
Tributary Areas
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Loadings for Roof Diaphragm

• The upper beam diagram is for loading in the
  2 direction.
• The lower beam diagram is for loading in the
  1 direction.
• The distributed loads equal the pressure times
  the tributary height of the exposed area.
• The unit shears equal the beam reaction divided
  by the length of the edge.

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Loadings for Floor Diaphragm

• Note that the unit shears at the ends of the
  diaphragm are the result of the interaction with
  the shear walls that are providing lateral
  support for the diaphragm.
• These forces are transferred to the shear walls.

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Elements for Direction 1
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Idealized Diagram for Dir. 1

• Green arrows are unit shears at edge of roof
  diaphragm.
• Yellow arrows are unit shears at edge of floor
  diaphragm.
• Shear in upper part of shear wall is from roof
  diaphragm only.
• Shear (red arrows )in lower part of shear wall
  includes both horizontal diaphragms.

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Shear Wall Free Body Diagram
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Elements for Direction 2
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Idealized Diagram for Dir. 2

• Green arrows are unit shears at edge of roof
  diaphragm.
• Yellow arrows are unit shears at edge of floor
  diaphragm.
• Shear in upper part of shear wall is from roof
  diaphragm only.
• Shear (red arrows )in lower part of shear wall
  includes both horizontal diaphragms.

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Shear Wall Free Body Diagram
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Another View
Amrhein, James E Reinforced Masonry Engineering
Handbook, 4th edition
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Diaphragms are Beams

• Like beams, diaphragms carry loads in bending.
• Wood diaphragms are considered to be simply
  supported.
• This results in both internal bending moment and
  shear.
• The diaphragm can be considered to be similar to
  a wide flange beam where the flanges (diaphragm
  chords) take all the bending and the web (the
  plywood sheathing) takes all the shear.
• In diaphragms, the shear force is expressed in
  terms of unit shear.

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Beam Behavior of Diaphragms
Amrhein, James E Reinforced Masonry Engineering
Handbook, 4th edition
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Diaphragm Forces in Dir. 1
C M / L1
M w(L2)2/8
v w(L2)/(2L1)
T M / L1

• Unit shear, v, equals the shear force, V, at a
  location along the span divided by the depth of
  the diaphragm at that location.
• Moment is taken by chord forces whose magnitudes
  equal the Moment at a particular location
  divided by the diaphragm depth at the same
  location.

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Diaphragm Forces in Dir. 2
v w(L2)/(2L1)

• The diaphragm must be analyzed and designed to
  handle the forces in both principle directions.

M
C M / L2
T M / L2
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Maximum Diaphragm Ratios2003 IBC

• IBC Table 2305.2.3 (text pg C.42) - Rules of
  Thumb used to control diaphragm deflections.
• If the span to width ratios are too large, then
  the diaphragm is not stiff enough to transfer the
  forces without significant deflection.
• Deflection is a function of beam bending, shear
  deflection, nail slip in diaphragm and slip in
  chord connections.

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Shear Capacity of Horizontal Wood Diaphragms2003
IBC

• UBC Table 2306.3.1 (pgs C.45-C.47)
• Also see Special Design Provisions for Wind
  Seismic Table A.4.2A
• Shear capacity depends on the following design
  variables
• supporting member species
• plywood grade
• nail size (and penetration)
• plywood thickness (normally selected for vert.
  loads)
• support widths
• nail spacing
• blocking
• layup

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Footnote a

• Use of supporting lumber species other than
  Douglas Fir or Southern Pine
• (1) find specific gravity of supporting framing
  (see NDS Table 11.3.2A, NDS pg 74)
• For Staples Use Structural I values multiplied
  by either 0.82 or 0.65 depending on specific
  gravity of supporting members.
• For Nails Use values from table for actual
  grade of plywood used multiplied by
  min(.5S.G),1

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Footnote b

• Field nailing requirement
• Spacing of fasteners along intermediate framing
  to be 12 O.C. unless supporting member spacing
  equals 48 or more, then use 6 O.C. nail spacing.

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Use With Wind Loads

• IBC-03 2306.3.1 states
• The allowable shear capacities in Table 2306.3.1
  for horizontal wood structural panel diaphragms
  shall be increased 40 percent for wind design

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Some Definitions

• Nailing
• Boundary nailing Nailing at all intersections
  with shear walls. (parallel to direction of
  force.)
• Edge nailing nailing along any other supported
  plywood edge.
• Field nailing nailing along supports but not at
  a plywood edge.
• Layup cases (See IBC Table 2306.3.1)

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Nailing Definitions
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Chord Design

• The chords are axial force members that generally
  have full lateral support in both principle
  directions.
• The top plates of the supporting walls are
  generally used as the chord members.
• Due to the reversing nature of the loads being
  resisted, the chord forces are considered to be
  both tension and compression.
• Design as an axial force member.

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Typical Chord

• Roof Chord Member

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Example

• Consider the building introduced in the lecture
  on structural behavior

We spent some time determining forces in the
horizontal and vertical diaphragms (shear walls)
in an earlier lecture.
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Applied Forces Wind
Direction 1 Roof 12,000 200 plf 2nd flr
6,300 105 plf
Direction 2 Roof 5,200 60 plf to 200
plf 2nd flr 4,200 105 plf
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Roof Diaphragm Direction 1

• Parameters
• ½ C-DX plywood
• 2x Hem Fir Framing
• Vmax 150 plf
• Case I layup
• Design nailing for the diaphragm (IBC)
• Unblocked, 8d nails
• Vallow 1.4240 (1-(.5-.43))
• Vallow 313 plf gt Vmax

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Roof Diaphragm Direction 2

• Parameters
• ½ C-DX plywood
• 2x Hem Fir Framing
• Vmax 43.3 plf
• Case 3 layup

• Design nailing for the diaphragm
• Unblocked, 8d nails
• Vallow 1.4180(1-(.5-.43))
• Vallow 234 plf gt Vmax

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Roof Diaphragm Sheathing Summary

• After determining the needs in each direction the
  design of the roof can be specified.

• Result
• ½ C-DX plywood
• Unblocked
• 8d _at_ 6 O.C. Edge and Boundary nailing
• 8d _at_ 12 O.C. Field nailing

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Roof Diaphragm Chords Direction 1

• Moment 90 ft-k
• Depth 40 ft
• Chord Force 2.25 k

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Roof Diaphragm Chords Direction 2

• Moment 82.7 ft-k
• Depth 60 ft
• Chord Force 1.38 k

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Chord DesignHem Fir 2

• Try (1) 2x4
• Check Tension
• Ft (525 psi)(1.6)(1.5)
• Ft 1260 psi
• ft 2250 / 5.25 in2
• ft 429 psi lt Ft

• Try (1) 2x4
• Check Compression
• Fc (1300 psi)(1.6)(1.15)
• Fc 2392 psi
• fc 2250 / 5.25 in2
• fc 429 psi lt Fc

(1) 2x4 is adequate in both directions